Abstract
We study the expansion of the eigenfunctions of Schrödinger operators with smooth confinement potentials in Hermite functions; confinement potentials are potentials that become unbounded at infinity. The key result is that such eigenfunctions and all their derivatives decay more rapidly than any exponential function under some mild growth conditions to the potential and its derivatives. Their expansion in Hermite functions converges therefore very fast, super-algebraically.
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This research was supported by the DFG-Priority Program 1324 and the DFG-Research Center Matheon.
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Gagelman, J., Yserentant, H. A spectral method for Schrödinger equations with smooth confinement potentials. Numer. Math. 122, 383–398 (2012). https://doi.org/10.1007/s00211-012-0458-8
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DOI: https://doi.org/10.1007/s00211-012-0458-8